A类算子n次根的代数扩张是次标量算子

Algebraic Extensions of nth Root of Class A Operators are Subscalar

研究了A类算子n次根的代数扩张.特别地,利用空间分解技巧得到每个A类算子n次根的代数扩张是次标量算子.作为应用,考虑了此类算子的Weyl型定理和超不变子空间问题.

Algebraic extension of nth root of class A operator is studied.Specifically,we obtain that every algebraic extension of nth root of class A operator is subscalar.The proof uses the space decomposition technique.As a consequence,we consider the Weyl type theorems and the hyperinvariant subspace for such operator.